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On p-Groups With Automorphism Groups Related To The Chevalley Group G2(p)

Let p be an odd prime. We construct a p-group P of nilpotency class two, rank seven and exponent p, such that Aut(P) induces NGL(7,p)(G2(p))=Z(GL(7,p))G2(p) on the Frattini quotient P/Φ(P). The constructed group P is the smallest p-group with these properties, having order p14, and when p=3 our construction gives two nonisomorphic p-groups. To show that P satisfies the specified properties, we study the action of G2(q) on the octonion algebra over Fq, for each power q of p, and explore the reducibility of the exterior square of each irreducible seven-dimensional Fq[G2(q)]-module.

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Judul Seri

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY; Vol.108 Issue 3 June 2020

No. Panggil

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Penerbit

: .,

Deskripsi Fisik

p. 321 - 331

Bahasa

English

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Klasifikasi

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Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

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Subjek

P-GROUP
EXTERIOR SQUARE
G2(Q)

Info Detail Spesifik

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Pernyataan Tanggungjawab

John Bamberg, Saul D, Freedman, Luke Morgan

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